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This study addresses the consensus problem for linear multi-agent systems subject to external disturbances under the leaderless framework. A novel distributed dynamic output feedback control protocol is proposed, which utilises not only relative output information of neighbouring agents but also relative state information of neighbouring controllers. Through model transformation, the consensus control problem of multi-agents network is reduced to a set of independent stabilisation subproblems for n-dimensional linear systems. Sufficient analysis conditions are derived using the Lyapunov method. An important contribution of this work lies in that the leaderless output-feedback consensus synthesis conditions are convexified without introducing any conservatism and formulated as linear matrix inequalities, which can be solved efficiently via convex optimisation. This is achieved by using a novel dynamic output-feedback controller structure. A numerical example has been used to demonstrate the advantage of theoretical results.